Newtons second law force problem

A 69 kg block is pushed along the celing with a constant applied force of 1300N that acts at an angle of 56 degrees with the horzontal. The block accelerates to the right at 8m/s^2. What is the magnitude of the normal force the ceiling exerts on the block? Answer in units of N.

and

A merry-go-round makes one complete revolution in 16s. A 19.7kg child sits on the horizontal floor of the merry-go-round 3.58 m from the center. Find the child's acceleration. Answer in units of m/s^2.

The child's mass is irrelevant. Since the radius for the child is 3.58 meters, the child is going around a distance of 2&pi; (3.58) meters every 16 s. From that you can determine the childs speed in mets per second. Of course that's a constant speed but the direction is changing. Do you have a formula for the the acceleration toward the center given the speed around the circle?